Root sentence example

root
  • I'll do new potatoes and roasted root vegetables.
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  • Its preamble stated that its object was " to exterminate the root and ground of this pest."
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  • I'd rather root them out and have them killed.
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  • The original root is seen in Skt.
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  • But none of these classifications of expense reaches the root of the matter.
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  • The right otocyst is seen at the root of the foot.
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  • It kills all root pests.
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  • Muscular substance forming the root of the foot.
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  • For such functions remain unaltered when each root receives the same infinitesimal increment h; but writing x-h for x causes ao, a1, a 2 a3,...
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  • The root of the tree is very strong and ramifying.
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  • But it took firm root on Norman soil; it made its way to England at an early stage of its growth, and from that time it went on developing and improving on both sides of the Channel till the artistic revolution came by which, throughout northern Europe, the Romanesque styles gave way to the Gothic. Thus the history of architecture in England during the 11th and 12th centuries is a very different story from the history of the art in Sicily during the same time.
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  • At the root of all economic investigation lies the conception of the standard of life of the community.
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  • This view of nature Bacon considered fundamental, and it lies, indeed, at the root of his whole philosophy.
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  • The first accurate description of the plant is given by Theophrastus, from whom we learn that it grew in shallows of 2 cubits (about 3 ft.) or less, its main root being of the thickness of a man's wrist and 10 cubits in length.
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  • From this root, which lay horizontally, smaller roots pushed down into the mud, and the stem of the plant sprang up to the height of 4 cubits, being triangular and tapering in form.
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  • Of the head nothing could be made but garlands for the shrines of the gods; but the wood of the root was employed in the manufacture of different utensils as well as for fuel.
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  • On the 4th of May Milner penned a memorable despatch to the Colonial Office, in which he insisted that the remedy for the unrest in the Transvaal was to strike at the root of the evil - the political impotence of the injured.
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  • It seems not unlikely that Pelagianism had taken root among the Christian communities of Ireland, and it was found necessary to send a bishop to combat the heresy.
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  • The equation then becomes a 2 /V = k, or a = A / Vk, so that the molecular conductivity is proportional to the square root of the dilution.
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  • From the first he ranged himself among the opponents of John of Gaunt, duke of Lancaster; he was a firm upholder of the rights of the English Church, and was always eager to root out Lollardry.
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  • The new creed, the new speech, the new social system, had taken such deep root that the descendants of the Scandinavian settlers were better fitted to be the armed missionaries of all these things than the neighbours from whom they had borrowed their new possessions.
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  • In germination of the seed the root of the embryo (radicle) grows out to get a holdfast for the plant; this is generally followed by the growth of the short stem immediately above the root, the so-called "hypocotyl," which carries up the cotyledons above the ground, where they spread to the light and become the first green leaves of the plant.
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  • A similar growth occurs in the root.
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  • This increase in the diameter of stem and root is correlated with the increase in leaf-area each season, due to the continued production of new leaf-bearing branches.
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  • The lower part of the trunk bears huge buttresses, each of which ends in a long branching far-spreading; root, from the branches of which spring the peculiar knees which, rise above the level of the water.
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  • The root appears more or less disguised in a vast number of river names all over the Celtic area in Europe.
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  • In Switzerland and parts of Germany, where it is collected in some quantity for commerce, a long strip of bark is cut out of the tree near the root; the resin that slowly accumulates during the summer is scraped out in the latter part of the season, and the slit enlarged slightly the following spring to ensure a continuance of the supply.
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  • Schultens (Vita Sal., Index geogr.) cites Tatmur as a variant of the Arabic name; this might mean " abounding in palms " (from the root tamar); otherwise Tadmor may have been originally an Assyrian name.
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  • Planters appreciate generally the value of broad-leaved and narrow-leaved plants and root crops, but there is an absence of exact knowledge, with the result that their practices are very varied.
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  • It is sometimes assumed that this is measured perfectly by the standard deviation,' which is obtained by taking the squares of the differences between the average and the individual prices, summing them and extracting the square root.
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  • He displayed his political tact in the choice of the American delegation, which was led by Secretary Hughes and included, besides Elihu Root, two members of the Senate, Lodge and Underwood, the Republican and Democratic leaders respectively.
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  • Since the current passing through the balance when equilibrium is obtained with a given weight is proportional to the square root of the couple due to this weight, it follows that the current strength when equilibrium is obtained is proportional to the product of the square root of the weight used and the square root of the displacement distance of this weight from its zero position.
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  • Each instrument is accompanied by a pair of weights and by a square root table, so that the product of the square root of the number corresponding to the position of the sliding weight and the ascertained constant for each weight, gives at once the value of the current in amperes.
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  • Worterbuch, who derives the element bel from an old Celtic root meaning shining, &c.) (W.
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  • This book evidently afforded the root idea of the Ignatian and more famous book.
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  • Farn; the Indo-European root, seen in the Sanskrit parna, a feather, shows the primary meaning; cf.
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  • It is closely related to the Manioc, cassava or tapioca plant (Manihot utilissima) which it resembles when young and exhibits a similar tuberous root system.
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  • After brushing away the loose stones and dirt from the root of the tree by means of a handful of twigs, the collector lays down large leaves for the latex to drop upon.
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  • The word is commonly used in the Alexandrian Greek translation of the Old Testament (Septuagint) for the Hebrew word (ger) which is derived from a root (gur) denoting to sojourn.
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  • Under cultivation this root becomes much enlarged, as in turnip, swede and others.
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  • In the case of the determinant of order 4 the square root is Al2A34 - A 13 A 24 +A14A23.
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  • The resultant being a product of mn root differences, is of degree mn in the roots, and hence is of weight mn in the coefficients of the forms; i.e.
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  • If Hebrew, it might be derived from the root p rr (to embrace) as an intensive term of affection.
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  • Both solea and solum are, of course, from the same root.
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  • But its linen manufactures, begun early in the 18th century, gradually restored prosperity; and when other industries had taken root its fortunes advanced by leaps and bounds, and there is now no more flourishing community in Scotland.
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  • Then moving farther in the same direction he resolved to strike at the root of the evil by the exercise of his imperial authority.
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  • In these haunts of learning the new studies took root after the year 1440, chiefly through the influence of travelling professors; Peter Luder and Samuel Karoch.
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  • In " Root rot," as the name implies, the roots are attacked, the fungus being a species of Ozonium, which envelops the roots in a white covering of mould or mycelium.
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  • The crown or upper portion of the root gives rise to new plants.
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  • When put to the lip, the juice of the aconite root produces a feeling of numbness and tingling.
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  • The horse-radish root, which belongs to the natural order Cruciferae, is much longer than that of the aconite, and it is not tapering; its colour is yellowish, and the top of the root has the remains of the leaves on it.
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  • They are easily propagated by divisions of the root or by seeds; great care should be taken not to leave pieces of the root about owing to its very poisonous character.
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  • From the root of Aconitum Napellus are prepared a liniment and a tincture.
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  • The action of aconitine on the circulation is due to an initial stimulation of the cardio-inhibitory centre in the medulla oblongata (at the root of the vagus nerves), and later to a directly toxic influence on the nerve-ganglia and muscular fibres of the heart itself.
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  • When the compass is far from the magnet, the vibrations will be comparatively slow; when it is near a pole, they will be exceedingly rapid, the frequency of the vibrations varying as the square root of the magnetic force at the spot.
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  • The long and bushy tail in the northern species has a white tip and a dark gland-patch near the root, but the backs of the ears are fawn-coloured.
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  • At their root lay a common Eastern origin rather than any borrowing.
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  • The great majority of the people are unused to wheaten bread, using the coarse flour of the mandioca root instead, consequently the demand for wheat and flour is confined to the large cities, which can obtain them from Argentina more cheaply than they can be produced in the country.
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  • Begun about 1880, this propaganda took deep root in the educated classes, creating a desire for change and culminating in the military conspiracy of November 1889, by which monarchy was replaced by a republican form of government.
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  • In Bosnia the persistent attempts of the Magyar princes to root out the stubborn, crazy and poisonous sect of the Bogomils had alienated the originally amicable Bosnians, and in 1353 Louis was compelled to buy the friendship of their Bar Tvrtko by acknowledging him as king of Bosnia.
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  • It took no root in the soil.
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  • The grammatical forms are expressed, as in Turkish, by means of affixes modulated according to the high or low vowel power of the root or chief syllables of the word to which they are appended-the former being represented by e, o, S, ii, i l l, the latter by a, d, o, 6, u, it; the sounds e, i, i are regarded as neutral.
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  • In n = a P, a is the root or base, p is the index or logarithm, and n is the power or antilogarithm.
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  • Denoting the root by a, and the number 2222222 in this scale by N, we have N = 2222222.
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  • But it may be shown that (r being > o) This only gives one root.
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  • The name l'arte magiore, the greater art, is designed to distinguish it from l'arte minore, the lesser art, a term which he applied to the modern arithmetic. His second variant, la regula de la cosa, the rule of the thing or unknown quantity, appears to have been in common use in Italy, and the word cosa was preserved for several centuries in the forms toss or algebra, cossic or algebraic, cossist or algebraist, &c. Other Italian writers termed it the Regula rei et census, the rule of the thing and the product, or the root and the square.
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  • Owing to the connexion of medicine with these seats of learning, it was natural that the study of the structure and functions of the human body and of the animals nearest to man should take root there; the spirit of inquiry which now for the first time became general showed itself in the anatomical schools of the Italian universities of the 16th century, and spread fifty years later to Oxford.
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  • In the first quadrant there is no root after zero, since tan u> u, and in the second quadrant there is none because the signs of u and tan u are opposite.
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  • The first root after zero is thus in the third quadrant, corresponding to m =1.
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  • Even in this case the series converges sufficiently to give the value of the root with considerable accuracy, while for higher values of m it is all that could be desired.
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  • When the trigeminus nerve is divided (Majendie), or when its root is compressed injuriously, say Iby a tubercular tumour, the cornea begins to show points of ulceration, which, increasing in area, may bring about total disintegration of the eyeball.
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  • The root of the French vine is attacked by the Phylloxera, but that of the American vine, whose epidermis is thicker, is protected from it.
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  • Haller's definition of irritability as a property of muscular tissue, and its distinction from sensibility as a property of nerves, struck at the root of the prevailing hypothesis respecting animal activity.
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  • In England his system took little root.
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  • The mere control of existing traffic, local street improvements and provision of new means of communication between casual points, were felt to miss the root of the problem, and in 1903 a Royal Commission was appointed to consider the whole question of locomotion and transport in London, expert evidence being taken from engineers, representatives of the various railway and other companies, of the County Council, borough councils and police, and others.
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  • When we remember that more than half of the area of London was occupied by these establishments, and that about a third of the inhabitants were monks, nuns and friars, it is easy to imagine how great must have been the disorganization caused by this root and branch reform.
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  • This is illustrated in the "harbinger of spring," a name given to a small plant belonging to the Umbelliferae, which has a tuberous root, and small white flowers; it is found in the central states of North America, and blossoms in March.
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  • Birdwood's force had taken root since April were spurs of a tangled mountain mass known as Sari Bair, from the topmost ridges of which the Straits about the Narrows were partially visible at a distance of 4 or 5 miles.
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  • Glas, perhaps derived from an old Teutonic root gla-, a variant of glo-, having the general sense of shining, cf.
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  • Mycelium of the fungus attacking root of vine (reduced).
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  • Portion of vine root, showing masses of fructification (perithecia) of the fungus (reduced).
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  • The plant is readily propagated by cuttings, a piece of the stem bearing buds at its nodes will root rapidly when placed in sufficiently moist ground.
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  • The roots were grown under exactly the same cultivation and conditions as a crop of mangel-wurzel - that is to say, they had the ordinary cultivation and manuring of the usual root crops.
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  • Pomegranate root, or, better, the sulphate of pelletierine in dose of 5 grains with an equal quantity of tannic acid, may be used to replace the male fern.
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  • It may be so compact that root development is checked or stopped altogether, in which case the plant suffers.
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  • A good soil should be deep to allow of extensive root development and, in the case of arable soils, easy to work with implements.
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  • This is due to the nitrogenous root residues left in the land.
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  • Early meanings of the root gild or geld were expiation, penalty, sacrifice or worship, feast or banquet, and contribution or payment; it is difficult to determine which is the earliest meaning, and we are not certain whether the gildsmen were originally those who contributed to a common fund or those who worshipped or feasted together.
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  • It may be the Spanish word for the hanging branches of a vine which strike root in the ground, or the name may have been given from a species of bearded fig-tree.
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  • A third variety of jalap known as woody jalap, male jalap, or Orizaba root, or by the Mexicans as Purgo macho, is derived from Ipomaea orizabensis, a plant of Orizaba.
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  • The root occurs in fibrous pieces, which are usually rectangular blocks of irregular shape, 2 in.
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  • It is the plural form of Targi," a raider."The Tawareq call themselves by some variant of the root MasheqTamasheq, Imoshagh, &c.
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  • The derivation of Yahweh from hawah is formally unimpeachable, and is adopted by many recent scholars, who proceed, however, from the primary sense of the root rather than from the specific meaning of the nouns.
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  • Two manuscripts, indeed, the British Museum and Mons texts, preserve a fragment relating the birth and infancy of the hero, which appears to represent the source at the root alike of Chretien and of the German Parzival, but it is only a fragment, and so far no more of the poem has been discovered.
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  • The probability seems to be that the earliest Perceval-Grail romance was composed at Fescamp, and was coincident with the transformation, under the influence of the Saint-Sang legend, of the originally Pagan talisman known as the Grail into a Christian relic, and that this romance was more or less at the root of all subsequent versions.
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  • He was fundamentally too much a man of strong convictions to be correctly described as open-minded, for if nature ever determined any man's faith, it was his; the root of his whole intellectual life, which was too deep to be disturbed by any superficial change in his philosophy, being the feeling for God.
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  • In algebra, if a be a real positive quantity and w a root of unity, then a is the amplitude of the product aw.
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  • It is found in the form of its acid potassium salt in many plants, especially in wood-sorrel (Oxalis acetosella) and in varieties of Rumex; as ammonium salt in guano; as calcium salt in rhubarb root, in various lichens and in plant cells; as sodium salt in species of Salicornia and as free acid in varieties of Boletus.
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  • The aim of the historical works is to show the necessary connexion between philosophical concepts and the age to which they belong; the same idea is at the root of his constructive speculation.
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  • This conception of the nature of the numina and man's relation to them is the root notion of the old Roman religion, and the fully-formed state cult of the di indigetes even at the earliest historical period, must have been the result of long and gradual development, of which we can to a certain extent trace the stages.
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  • These confessions teach the root idea of Calvin's theology, the immeasurable awfulness of God, His eternity, and the immutability of His decrees.
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  • To remedy the evil, Casimir drew up and promulgated the severe statute of Great Poland, which went to the very root of the matter and greatly strengthened the hands of the king's justices.
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  • The meaning of the root from which it is derived is very doubtful; cf.
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  • Skeat refers it to a root meaning "to kill," which may connect it with Gr.
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  • During the summer they need considerable heat, all the light possible and plenty of air; in winter a temperature of 45° or 50° will be sufficient, and they must be kept tolerably dry at the root.
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  • Under- (Radicola) of Phylloxera, with proneath, between the legs, lies the boscis inserted into tissue of root rostrum, which reaches back to of vine.
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  • The insect is fixed by this rostrum, which is inserted into the root of the vine for the purpose of sucking the sap. The abdomen consists of seven segments, and these as well as the anterior segments bear four rows of small tubercles on their dorsal surface.
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  • The root kol is common to all the Teutonic nations, while in French and other Romance languages derivatives of the Latin carbo are used, e.g.
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  • In this sense modern philosophy had a common root in revolt against medievalism.
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  • It was, however, Berkeley who first sought to utilize the conclusions that were implicit in Locke's starting-point to disprove " the systems of impious and profane persons which exclude all freeedom, intelligence, and design from the formation of things, and instead thereof make a selfexistent, stupid, unthinking substance the root and origin of all beings."
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  • Hence, whatever we begin by saying, we must ultimately say ` mind ' " (Caird, Kant, 1.443) While the form in which these doctrines were stated proved fatal to them in the country of their birth, they took deep root in the next generation in English philosophy.
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  • In taking root in England idealism had to contend against the traditional empiricism represented by Mill on the one hand and the pseudo-Kantianism which was rendered current by Mansel and Hamilton on the other.
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  • While the English plantations were striking root along the coast, by somewhat prosaic but fruitful industry, and were growing in population with rapid strides, two other movements were in progress.
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  • In 662 he was again brought to Constantinople and was condemned by a synod to be scourged, to have his tongue cut out by the root, and to have his right hand chopped off.
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  • That world of the learned offers us non-dogmatic definitions, drawn up from the outside; definitions which do not share the root assumptions either of Catholicism or of post-Reformation Protestant orthodoxy.
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  • Under the empire we find Eastern cults taking root here sooner than in Rome.
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  • These lines isolate certain swellings or monticuli, the largest of which is (I) the ball of the thumb, called the mountain of Venus; (2) that at the base of the index finger is the mountain of Jupiter; (3) at the root of the middle finger is the mountain of Saturn, while those at the bases of ring and little finger are respectively the mountains of the (4) Sun and (5) of Mercury.
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  • This sentence from Browne's spiritual autobiography contains the root of the whole matter, and explains the title of his other chief work, also of 1582, A Treatise of Reformation without tarrying for any, and of the wickedness of those Preachers which will not reform till the Magistrate command or compel them.
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  • Haue; the root is seen in "hew," to cut, cleave; the word must be distinguished from "hoe," promontory, tongue of land, seen in place names, e.g.
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  • Several types of horse-drawn hoe capable of working one or more rows at a time are used among root and grain crops.
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  • Blue flag, snake root, ginseng, lobelia, tansy, wormwood, wintergreen, pleurisy root, plantain, burdock, sarsaparilla and horehound are among its medicinal plants.
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  • The etymology of the word is uncertain, but it has been taken to be connected with a root meaning "to twist."
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  • The real root of the difficulty to Platonist as to Gnostic was his sharp antithesis of form as good and matter as evil.
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  • In 1841 Father Peter John De Smet (1801-1872), a Belgian Jesuit missionary established Saint Mary's Mission in Bitter Root Valley, but, as the Indians repeatedly attacked the mission, it was abandoned in 1850.
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  • More probably, however, this is but an accidental coincidence; both adam and adamu may come from the same Semitic root meaning "to make."
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  • This being the root and origin of their power, renders them responsible to the party from whom all their immediate or consequential powers are derived."
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  • The etymology of rivus and ripa is disputed; some scholars refer both to the root ri-, to drop, flow; others take ripa to be from the root seen in Gr.
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  • It is doubtful whether this root meant originally to " cover " or " wipe out "; but probably it is used as a technical term without any consciousness of its etymology.
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  • The keynote of his History is contained in his assertion that the Reformation was "the root and source of the expansive force which has spread the Anglo-Saxon race over the globe."
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  • Perkin also had a large share in the introduction of artificial alizarin, the red dye of the madder root.
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  • Bedier, is that there was one poem, and one only, at the root of the various versions preserved to us, and that that poem, composed in England, probably by an AngloNorman, was a work of such force and genius that it determined for all time the form of the Tristan story.
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  • Razin proclaimed that his object was to root out the boyars and all officials, to level all ranks and dignities, and establish Cossackdom, with its corollary of absolute equality, throughout Muscovy.
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  • In 1842 Hammer-Purgstall correctly explained the name as meaning the "warm-flowing" (tab= warm, same root as tep in "tepid") from some warm mineral springs in the neighbourhood, and compared it with the synonymous Teplitz in Bohemia.
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  • Philo, De posteriori Caini, § 3, explains the name as meaning iroru ryos,"watering" or "irrigation," connecting it with the Hebrew root Sh Th Josephus, Ant.
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  • This called forth a letter' from St Paul, who felt himself compelled to grapple at close quarters with teaching which he saw cut at the very root of his own.
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  • The small ratio, or ratiuncula, is in fact that of the millionth root of to to unity, and if we denote it by the ratio of a to 1, then the ratio of 2 to I will be nearly the same as that of a301'°30 to i, and so on; or, in other words, if a denotes the millionth root of 10, then 2 will be nearly equal to a 301,030, 3 will be nearly equal to a477,1u, and so on.
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  • He then by means of a simple proportion deduced that log (I 00000 00000 00000 I)=o 00000 00000 00000 0 434 2 944 81 90325 1804, so that, a quantity 1.00000 00000 00000 x (where x consists of not more than seventeen figures) having been obtained by repeated extraction of the square root of a given number, the logarithm of I 00000 00000 00000 x could then be found by multiplying x by 00000 00000 00000 04342 To find the logarithm of 2, Briggs raised it to the tenth power, viz.
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  • Adding the characteristic 3, and dividing by 10, he found (since 2 is the tenth root of 1024) log 2 = 30102 9995 6 63981 195.
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  • In Gnosticism salvation always lies at the root of all existence and all history.
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  • A comparatively new product in this region is that of canaigre, which is grown for the tannin found in its root.
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  • The natural and forest products of Mexico include the agave and yucca (ixtle) fibres already mentioned; the " ceibon " fibre derived from the silk-cotton tree (Bombax pentandria); rubber and vanilla in addition to the cultivated products; palm oil; castor beans; ginger; chicle, the gum extracted from the " chico-zapote " tree (Achras sapota); logwood and other dye-woods; mahogany, rosewood, ebony, cedar and other valuable woods; " cascalote " or divi-divi; jalap root (Ipomaea); sarsaparilla (Smilax); nuts and fruits.
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  • It must have reality for itself, a reality which stands in no'conflict with its ideal character, a reality the inner structure of which is ideal, a reality the root and spring of which is spirit.
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  • The general or typical coloration is, however, a rich tan upon the head, neck, body, outside of legs, and tail near the root.
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  • The tail has large black spots near the root, some with light centres, and from about midway of its length to the tip it is ringed with black.
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  • The bark, of nearly the same tint as that of the redwood, is extremely thick and is channelled towards the base with vertical furrows; at the root the ridges often stand out in buttress-like projections.
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  • The average length is about 40 in., and the general tone of colour tawny mingled with black and white above and whitish below, the tail having a black tip and likewise a dark glandpatch near the root of the upper surface.
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  • Potatoes and turnips are the only root crops that succeed, and barley and oats are grown in some of the islands.
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  • This idea that to partake of sacrifice is to devote oneself to the deity, lies at the root of the ancient idea of worship, whether Jewish or heathen; and St Paul uses it as being readily understood.
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  • In England, during the religious changes of the 16th century, such of these customs as had already taken root were abolished; and with them the practice of reserving the Eucharist in the churches appears to have died out too.
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  • The old hand-mill was known as a " quern," a word which appears in this sense in many Indo-European languages; the ultimate root is gar-, to grind.
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  • Its numerous root extractions amply justify a stronger expression than " multo labore," especially in an epitaph.
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  • In 1873 Charles Hermite proved that the base of the Napierian logarithms cannot be a root of a rational algebraical equation of any degree.3 To prove the same proposition regarding 7r is to prove that a Euclidean construction for circle-quadrature is impossible.
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  • The word was derived in antiquity from the town of Helos in Laconia, but is more probably connected with 'Aos, a fen, or with the root of AEiv, to capture.
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  • Practically the only grain crops that are cultivated are oats (which greatly predominate) and barley, while the favoured root crops are turnips (much the most extensively grown) and potatoes.
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  • The root of the wild plant is preferred to that of cultivated ginseng, and the older the plant the better is the quality of the root considered to be.
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  • The account given by Koempfer of the preparation of nindsin, the root of Sium ninsi, in Korea, will give a good idea of the preparation of ginseng, ninsi being a similar drug of supposed weaker virtue, obtained from a different plant, and often confounded with ginseng.
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  • The taste is mucilaginous, sweetish and slightly bitter and aromatic. The root is frequently forked, and it is probably owing to this circumstance that medicinal properties were in the first place attributed to it, its resemblance to the body of a man being supposed to indicate that it could restore virile power to the aged and impotent.
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  • The cover of the root, according to its quality, was silk, either embroidered or plain, cotton cloth or paper."
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  • The dose of the root is from 60 to 90 grains.
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  • The powdered root of P. roseum and other species is used in the manufacture of insect powders.
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  • In Tirol, a single hole is made near the root of the tree in the spring; this is stopped with a plug, and the turpentine is removed by a scoop in the autumn; but each tree yields only from a few ounces to z lb by this process.
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  • The trees for a considerable period show little sign of unhealthiness, but eventually the stem begins to swell somewhat near the root, and the whole tree gradually goes off as the disease advances; when cut down, the trunk is found to be decayed at the centre, the " rot " usually commencing near the ground.
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  • The expanded anterior root of the zygomatic process has its front border oblique.
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  • The front root of the zygomatic arch is nearly vertical, and placed so far back that it is above the second molar, while the orbit - a unique feature among rodents - is almost completely surrounded by bone.
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  • Projecting brows, deeply sunk dark eyes, short noses, either straight or arched, but 'always depressed at the root, and moderately thick lips, with a somewhat receding chin, are general characteristics.
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  • The present writer, therefore, in his Theory of Optics, adopted different names, and called the series respectively the " Trunk," the " Main Branch " and the " Side Branch," the main branch being identical with the second subordinate series; the limit of frequency for high values of s is called the " root " of the series, and it is found in all cases that the two branches have a common root at some point in the trunk.
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  • According to an important law discovered by Rydberg and shortly afterwards independently by the writer, the frequency of the common root of the two branches is obtained by subtracting the frequency of the root of the trunk from that of its least refrangible and strongest member.
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  • In the spectra of the alkali metals each line of the trunk is a doublet, and we may speak of a twin trunk springing out of the same root.
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  • There are, therefore, two main branches and two side branches, but these are not twins springing out of the same root, but parallel branches springing out of different though closely adjacent roots.
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  • C. Pickering discovered in the structure of the star E Puppis a series of lines which showed a remarkable similarity to that of hydrogen having the same root.
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  • Lord Rayleigh,' who has also investigated vibrating systems giving series of lines approaching a definite limit of " root," remarks that by dynamical reasoning we are always led to equations giving the square of the period and not the period, while in the equation representing spectral series the simplest results are obtained for the first power of the period.
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  • Equations of this form have received a striking observational verification in so far as they predict a tail or root towards which the lines ultimately tend when s is increased indefinitely.
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  • The ultimate origin is usually taken to be the root men-, to think, the root of "mind."
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  • The geometrical mean of n quantities is the nth root of their product.
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  • The quadratic mean of n quantities is the square root of the arithmetical mean of their squares.
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  • Thus a West African native who wants a suhman takes a rudely-cut wooden image or a stone, a root of a plant, or some red earth placed in a pan, and then he calls on a spirit of Sasabonsum ("a genus of deities, every member of which possesses identical characteristics") to enter the object prepared, promising it offerings and worship. If a spirit consents to take up its residence in the object, a low hissing sound is heard, and the suhman is complete.
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  • From the root of the kalo is made the national dish called poi; after having been baked and well beaten on a board with a stone pestle it is made into a paste with water and then allowed to ferment for a few days, when it is ready to be eaten.
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  • Again the root difference between the Presbyterian and Episcopalian conceptions of the church comes to light.
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  • Kant's a priori synthesis of sensations into experience lies at the root of all German idealism.
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  • As lack of insight lay at the root of their troubles, it was not enough simply to enjoin the moral fidelity to conviction which is three parts of faith to the writer, who has but little sense of the mystical side of faith, so marked in Paul.
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  • This has been partly preserved in some of their literary remains, and has taken deep root in the beliefs and traditions of the Bulgarians and other nations with whom they had come into close contact.
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  • How clearly he read the causes of religious decadence, how deeply he himself was convinced of the need of trenchant reform, is best shown by his instructions to Chieregati, his nuncio to Germany, in which he laid the axe to the root of the tree with unheard-of freedom.
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  • The head is mesati-cephalic, verging on brachycephalic in the case of many of the Dokpa; the hair is black and somewhat wavy; the eyes are usually of a clear brown, in some cases even hazel; the cheek-bones are high, but not so high as with the Mongols; the nose is thick, sometimes depressed at the root, in other cases prominent, even aquiline, though the nostrils are broad.
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  • The worship of images never seems to have taken root among Armenians; indeed they supplied the Greek world with iconoclast soldiers and emperors.
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  • While discussing noses, he says that those with thick bulbous ends belong to persons who are insensitive, swinish; sharp-tipped belong to the irascible, those easily provoked, like dogs; rounded, large, obtuse noses to the magnanimous, the lion-like; slender hooked noses to the eagle-like, the noble but grasping; round-tipped retrousse noses to the luxurious, like barndoor fowl; noses with a very slight notch at the root belong to the impudent, the crow-like; while snub noses belong to persons of luxurious habits, whom he compares to deer; open nostrils are signs of passion, &c.
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  • The root of this plant, when eaten by white pigs, caused their bones to turn to a pink colour and their hoofs to fall off, but the black pigs could eat the same plant with impunity.
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  • The real meaning of the word `ibhri must ultimately be sought in the root `abhar, to pass across, to go beyond, from which is derived the noun `ebher, meaning the " farther bank " of a river.
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  • In the latter part of the word we have, of course, the same root as in caedere, " to kill," but whether or not the former part is from pater, " a father," or from the same root that we have in per-peram, per-jurium, is a moot point.
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  • It took root and spread in spite of opposition until 1864, when an anti-foreign outbreak exterminated it.
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  • The derivation of the name Alps is still very uncertain, some writers connecting it with a Celtic root alb, said to mean height, while others suggest the Latin adjective albus (white), referring to the colour of the snowy peaks.
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  • The root, though not precluded from access of air, is not directly dependent for its growth on the agency of light.
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  • Nutrition (assimilation) by the leaves includes the inhalation of air, and the interaction under the influence of light and in the presence of chlorophyll of the carbon dioxide of the air with the water received from the root, to form carbonaceous food.
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  • It is a matter of familiar observation that the ends of the shoots of brambles take root when bent down to the ground.
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  • A diminished supply of water at the root is requisite, so as to check energy of growth, or rather to divert it from leaf-making.
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  • If they spring from a thick root it is not to be wantonly severed, but the soil should be removed and the sucker taken off by cutting away a clean slice of the root, which will then heal and sustain no harm.
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  • For propagation the bulbiferous portion is pegged down on the surface of a pot of suitable soil; if kept close in a moist atmosphere, the little buds will soon strike root and form independent plants.
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  • Some plants root so freely that they need only pegging down; but in most cases the arrest of the returning sap to form a callus, and ultimately young roots, must be brought about artificially, either by twisting the branch, by splitting it, by girding FIG.
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  • One whole summer, sometimes two, must elapse before the layers will be fully rooted in the case of woody plants; but such plants as carnations and picotees, which are usually propagated in this way, in favourable seasons take only a few weeks to root, as they are layered towards the end of the blooming season in July, and are taken off and planted separately early in the autumn.
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  • In this case the scion is grafted directly on to a portion of the root of some appropriate stock, both graft and stock being usually very small; the grafted root is then potted so as to cover the point of junction with the soil, and is plunged in the bed of the propagating house, where it gets the slight stimulus of a gentle bottom heat.
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  • Trees to be grown in the form of a bush are usually budded low down on the stem of the stock as near the root as possible to obviate the development of wild suckers later on.
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  • These are cut up into half-inch lengths (more or less), and inserted in light sandy soil round the margin of a cutting pot, so that the upper end of the root cutting may be level with the soil or only just covered by it.
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  • The tree will then be ready to lift if carefully prized up from beneath the ball, and if it does not lift readily, it will probably be found that a root has struck downwards, which will have to be sought out and cut through.
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  • The plants should be prepared for this by keeping them rather dry at the root, and after cutting they must stand with little or no water till the stems heal over, and produce young shoots, or " break," as it is technically termed.
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  • The advantages of the operation may generally be gained by judicious root pruning, and it is not at all adapted for the various stone fruits.
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  • Ferns should not be allowed to become quite dry at the root, and the water used should always be at or near the., temperature of the house in which the plants are growing.
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  • These should be kept cut off close to the old plant, so that the full force of the root is expended in making the " crowns " or fruit buds for next season's crop. If plants are required for new beds, only the required number should be allowed to grow, and these may be layered in pots as recommended in July.
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  • The "Old Catholic" party, under the bishop of Bonn, has failed, despite its early successes, to take deep root in the country.
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  • The root from which these words derive is that of "give."
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  • As the kingdom had not come, it was assumed that there must be persons living who had been present at the crucifixion; the same reasoning is at the root of the Anglo-Israel belief.
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  • Many fungi (Phallus, Agaricus, Fumago, &c.) when strongly growing put out ribbon-like or cylindrical cords, or sheet-like mycelial plates of numerous parallel hyphae, all growing together equally, and fusing by anastomoses, and in this way extend long distances in the soil, or over the surfaces of leaves, branches, &c. These mycelial strands may be white and tender, or the outer hyphae may be hard and black, and very often the resemblance of the subterranean forms to a root is so marked that they are termed rhizomorphs.
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  • Infection in these cases occurs in the seedling at the place where root and shoot meet, and the infecting hypha having entered the plant goes on living in it and growing up with it as if it had no parasitic action at all.
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  • Thus, in Sumerian we find such forms as numunnib-bi, " he speaks not to him," where the negative prefix nu and the verbal prefix mun are in harmony, but in dissimilation to the infix nib, " to him," and to the root bi, " speak," which are also in harmony.
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  • For example, an indeterminative vowel, a, e, i or u, may be prefixed to any root to form an abstract; thus, from me, " speak," we get e-me, " speech"; from ra, " to go," we get a-ra, " the act of going," &c. In connexion with the very complicated Sumerian verbal system 2 it will be sufficient to note here the practice of infixing the verbal object which is, of course, absolutely alien to Semitic. This phenomenon appears also in Basque and in many North American languages.
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  • Used for muffs, trimmings, boas, and carriage 1 The measurements given are from nose to root of tail of average large sizes after the dressing process, which has a shrinking tendency.
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  • Socialism of a German type had taken deep root among the working men of the Flemish towns, especially at Ghent and Brussels; socialism of a French revolutionary type among the Walloon miners and factory hands.
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  • Digitonin, on the other hand, is a cardiac depressant, and has been found to be identical with saponin, the chief constituent of senega root.
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  • The grains of both are very small, only one half as long as those of common millet, but are exceedingly prolific. Many stalks arise from a single root, and a single spike often yields 2 oz.
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  • The wood-vessels form part of the fibro-vascular bundles or veins of the leaf and are continuous throughout the leaf-stalk and stem with the root by which water is absorbed from the soil.
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  • The water taken up by the root from the soil contains nitrogenous and mineral salts which combine with the first product of photo-synthesis - a carbohydrate - to form more complicated nitrogen-containing food substances of a proteid nature; these are then distributed by other elements of the vascular bundles (the phloem) through the leaf to the stem and so throughout the plant to wherever growth or development is going on.
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  • If the effects depended merely on the velocity of translation of the molecules, both conductivity and viscosity should increase directly as the square root of the absolute temperature; but the mean free path also varies in a manner which cannot be predicted by theory and which appears to be different for different gases (Rayleigh, Proc. R.S., January 1896).
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  • He was a great opponent of university reform and of the Hegelianism which was then beginning to take root in Oxford.
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  • Although by no means fertile, the Erzgebirge is very thickly peopled, as various branches of industry have taken root there in numerous small places.
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  • Torn by dissensions the Teutonic Order was unsuccessful in checking the encroachments of the Poles, and in 1466 the land which it had won in the north-east of Germany passed under the suzerainty of Poland, care being taken to root out all traces of German influence therein.
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  • The popular feeling for the first time found expression when Luther, on All Saints day 1517, nailed to a church door in Wittenberg the theses in which he contested the doctrine Luther which lay at the root of the scandalous traffic in indulgences carried on in the popes name by Tetzel and his like.
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  • A fragment of a Welsh poem seems to confirm this tradition, which certainly lies at the root of her later abduction by Meleagaunt.
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  • Isobutyric acid is found in the free state in carobs (Ceratonia siliqua) and in the root of Arnica dulcis, and as an ethyl ester in croton oil.
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  • Saint Paul's visit to Syracuse naturally gave rise to many legends; but the Christian church undoubtedly took early root in Sicily.
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  • The widespread opinion that this sense first asserted itself in reference to the Arab root aj+ (faraqa), " sever," or " decide," is open to considerable doubt.
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  • From the root idea of obligation to serve or give something in return, involved in the conception of duty, have sprung various derivative uses of the word; thus it is used of the services performed by a minister of a church, by a soldier, or by any employee or servant.
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  • The same root kar leads through something like kar-kar-ta, glakarta (glazard in Breton), to lacerta and to "lizard."
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  • In later times the moral ct of his tale was doubtless the main cause of its continued alarity; Osiris was named Onnophris, the good Being excellence, and Seth was contrasted with him as the author the root of all evil.
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  • The typical Coptic root thus became biliteral rather than triliteral, and the verb, by means of periphrases, developed tenses of remarkable precision.
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  • Thus the tonus of the motor neurons of the spinal cord is much lessened by rupture of the great afferent root cells which normally play upon them.
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  • The familiar duckweed which covers the surface of a pond consists of a tiny green "thalloid" shoot, one, that is, which shows no distinction of parts - stem and leaf, and a simple root growing vertically downwards into the water.
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  • In Dicotyledons the shoot of the embryo is wholly derived from the terminal cell of the pro-embryo, from the next cell the root arises, and the remaining ones form the suspensor.
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  • In many Monocotyledons the terminal cell forms the cotyledonary portion alone of the shoot of the embryo, its axial part and the root being derived from the adjacent cell; the cotyledon is thus a terminal structure and the apex of the primary stem a lateral one - a condition in marked contrast with that of the Dicotyledons.
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  • The aim of germination is the fixing of the embryo in the soil, effected usually by means of the root, which is the first part of the embryo to appear, in preparation for the elongation of the epicotyledonary portion of the shoot, and there is infinite variety in the details of the process.
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  • Where detachable buds are produced, which can be transported through the air to a distance, each of them is an incipient shoot which may have a root, and there is always reserve-food stored in some part of it.
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  • It is based upon the fact that the histological differentiation of the epidermis of their root is that generally characteristic of Monocotyledons, whilst they have two cotyledons - the old view of the epiblast as a second cotyledon in Gramineae being adopted.
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  • He did much too for the economic development of Prussia, especially for agriculture; he established colonies, peopling them with immigrants, extended the canal system, drained and diked the great marshes of the Oderbruch, turning them into rich pasturage, encouraged the planting of fruit trees and of root crops; and, though in accordance with his ideas of discipline he maintained serfdom, he did much to lighten the burdens of the peasants.
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  • The absence of differentiation into root, stem and leaf which prevails among seaweeds, seems, for example, to have led Linnaeus to employ the term in the Genera Plantarum for a sub-class of Cryptogamia, the members of which presented this character in a greater or less degree.
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  • Fungi Algae Bryophyta Pteridophyta Phanerogamia Gymnosperms Angiosperms Algae in this wide sense may be briefly described as the aggregate of those simpler forms of plant life usually devoid, like the rest of the Thallophyta, of differentiation into root, stem and leaf; but, unlike other Thallophyta, possessed of a colouring matter;.
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  • In the case of an axial moment, the square root of the resulting mean square is called the radius of gyration of the system about the axis in question.
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  • If the quadratic (38) has a negative root, the trigonometrical functions in (36) are to be replaced by real exponentials, and the position x=o, y=o is unstable.
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  • For any particular root, the equations (5) determine the ratios of the quantities Af, A1,.
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  • The sectarial mark of the Ramanujas resembles a capital U (or, in the case of another division, a Y), painted with a white clay called gopichandana, between the hair and the root of the nose, with a red or yellow vertical stroke (representing the female element) between the two white lines.
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  • The sectarial mark of the adherents consists of two red perpendicular lines, meeting in a semicircle at the root of the nose, and having a round red spot painted between them.
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  • Once root out abuses with a firm hand, and they believed that a few timely concessions on points of doctrine would tempt most Protestants back within the Roman pale.
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  • Teresa turned to the mystical writers, and learnt from them how to root out the last relics of self-love from the mind by a long discipline of mystical trance and " contemplation."
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  • Sidney followed with the sestine and terza rima and with various experiments in classic metres, none of which took root on English soil.
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  • The botanist Clusius (Charles de l'Escluse or Lecluse, 1526-1609) first cultivated it at Vienna from a root received from Asia Minor in 1574, and distributed it to other botanists in central and western Europe, and it was probably introduced into England about 1596 by the herbalist Gerard.
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  • The general colour of the fur is greyish, with a deep tinge of chestnut from the middle of the back to the root of the tail.
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  • An agitation against patronage, the ancient root of evil, and the formation of an antipatronage society, helped in the same direction.
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  • If we imagine the current in the conductor to be instantaneously reversed in direction, the magnetic force surrounding it would not be instantly reversed everywhere in direction, but the reversal would be propagated outwards through space with a certain velocity which Maxwell showed was inversely as the square root of the product of the magnetic permeability and the dielectric constant or specific inductive capacity of the medium.
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  • Flax is always pulled up by the root, and under no circumstances is it cut or shorn like cereal crops.
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  • The root idea seems to be that something is marked off as to be shunned, with the added hint of a mystic sanction or penalty enforcing the avoidance.
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  • The plants have a large rosette of thick fleshy leaves generally ending in a sharp point and with a spiny margin; the stout stem is usually short, the leaves apparently springing from the root.
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  • Perhaps the most constant and obvious distinction between this species and the next is the arrangement of the stripes on the hinder part of the back, where there are a number of short transverse bands reaching to the median longitudinal dorsal stripe, and unconnected with the uppermost of the broad stripes which pass obliquely across the haunch from the flanks towards the root of the tail.
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  • Snow-Harris found that this charge varied as the square root of the weight in the opposite pan, thus showing that the 1 It is probable that an experiment of this kind had been made as far back as 1746 by Daniel Gralath, of Danzig, who has some claims to have suggested the word " electrometer " in connexion with it.
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  • And looking back upon that course afterwards, he records with much complacency how his earliest St Andrews sermon built up a whole fabric of aggressive Protestantism upon Puritan theory, so that his startled hearers muttered, "Others sned (snipped) the branches; this man strikes at the root."
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  • Trametes radiciperda attacks the roots and penetrates to the stem, causing rotting of the wood; the disease is difficult to eradicate, as the mycelium of the fungus travels from root to root in the soil.
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  • Rotting of the wood at the base of the trunk is also caused by Agaricus melleus, which spreads from root to root in the soil by means of its long purple-black, cord-like mycelial strands known as Rhizomorpha.
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  • Closely allied to the Scotch pine, and perhaps to be regarded as a mere alpine form of that species, is the dwarf P. montana (or P. Pumilio), the " kummholz " or " knieholz " of the Germans - a recumbent bush, generally only a few feet high, but with long zigzag stems, that root occasionally at the knee-like bends where they rest upon the ground.
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  • Lagrange used simple continued fractions to approximate to the solutions of numerical equations; thus, if an equation has a root between two integers a and a+1, put x=a+I/y and form the equation in y; if the equation in y has a root between b and b+i, put y = b + I /z, and so on.
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  • The value of such a fraction is the positive root of a quadratic equation whose coefficients are real and of which one root is negative.
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  • Thus a strong Persian propagandism arose especially in Armenia and Cappadocia, where the religion took deep root among the people, but also in Lydia and Lycia.
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  • The therapeutic measures employed in these different cases may be directed towards alleviating the symptoms, such as itching, pain, cough and swelling, in which case the treatment will be merely symptomatic; or they may be directed towards removing the root of the disease, viz.
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  • Israel or distinguished Israelites, the root being the same as in Jeshurun; (2) that Jashar (" lc) is a transposition of shir C, song); (3) that it should be pointed Yashir (W, sing; cf.
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  • When boiled in water the root affords a dark extractive matter, the quantity of extract yielded by the root being used as a criterion of its quality.
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  • Boiling alcohol extracts from the root a neutral substance in the form of crystalline prisms, which crystallize in scales from boiling water.
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  • The presence in the root of starch, resin and oxalate of lime is revealed by the use of the microscope.
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  • The root bark is reddish-brown, thin and shrivelled, and there is an abundance of rootlets, which are technically known by the name of "beard."
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  • The bark is thick and furrowed, and of a pale fawn colour internally; the rootlets are few, and the root itself is of larger diameter than in the other kinds.
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  • The collection of sarsaparilla root is a very tedious business; a single root takes an Indian half a day or sometimes even a day and a half to unearth.
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  • A plant four years old will yield 16 lb of fresh root, and a well-grown one from 32 to 64 lb, but more than half the weight is lost in drying.
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  • The more slender roots are generally left, and the stem is cut down near to the ground, the crown of the root being covered with leaves and earth.
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  • These tubers form a considerable article of trade in China, but are used to a limited extent only on the Continent, under the name of China root, although introduced into Europe about the same time as sarsaparilla.
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  • He did not fail, however, to recognize also that the controversies frequently had their root in mere emulation, slander and sophistry.
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  • For a given fluid and a given orifice the length is approximately proportional to the square root of the head.
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  • The pitch of the note, though not absolutely definite, cannot differ much from that which corresponds to the division of the jet into wave-lengths of maximum instability; and, in fact, Savart found that the frequency was directly as the square root of the head, inversely as the diameter of the orifice, and independent of the nature of the fluid - laws which follow immediately from Plateau's theory.
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  • The interval from one swelling to the next is the space described by the drop during one complete vibration,and is therefore (as Plateau shows) proportional ceteris paribus to the square root of the head.
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  • The time of vibration is of course itself a function of the nature of the fluid and of the size of the drop. By the method of dimensions alone it may be seen that the time of infinitely small vibrations varies directly as the square root of the mass of the sphere and inversely as the square root of the capillary tension; and it may be proved that its expression is - V C?
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  • By screening the various parts with metallic plates in connexion with earth, Beetz further proved that, contrary to the opinion of earlier observers, the seat of sensitiveness is not at the root of the jet where it leaves the orifice, but at the place of resolution into drops.
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  • An easy way of testing this conclusion is to excite the extreme tip of a glass rod, which is then held in succession to the root of the jet, and to the place of resolution.
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  • When the orifice is circular of radius a, the limiting value of a is 1 J' z, where z is the least root of the equation FIG.
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  • Conversely, it was Paul's lack in this respect which lay at the root of his difficulties as an apostle.
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  • These enter the root-hairs of leguminous plants, and passing down the hair in the form of a long, slimy (zoogloea) thread, penetrate the tissues of the root.
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  • Judaism Rutilius could assail without wounding either pagans or Christians, but he intimates, not obscurely, that he hates it chiefly as the evil root whence the rank plant of Christianity had sprung.
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  • Root & Co., wholesale paper dealers in New York City, who failed in the following year.
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  • Field & Co., and in 1853 had accumulated $250,000, paid off the debts of the Root company and retired from active business, leaving his name and $100,000 with the concern.
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  • This animal, also called the bear-cat, is allied to the palm-civets, or paradoxures, but differs from the rest of the family (Viverridae) by its tufted ears and long, bushy, prehensile tail, which is thick at the root and almost equals in length the head and body together (from 28 to 33 inches).
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  • The Indo-European root is seen in Lat.
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  • The growth of the primary root is limited; sooner or later adventitious roots develop from the axis above the radicle which they ultimately exceed in growth.
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  • The entire spikelet, or single flowers, are transformed into small-leaved shoots which fall from the axes and readily root in the ground.
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  • Instability, again, which lies at the root of Spencer's definition "continuous adjustment of internal relations to external relations" is displayed by living matter in very varying degrees from the apparent absolute quiescence of frozen seeds to the activity of the central nervous system, whilst there is a similar range amongst inorganic substances.
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  • From analyses of the leaves, bark and root, it appears that quinine is present only in small quantities in the leaves, in larger quantity in the stem bark, and increasing in proportion as it approaches the root, where quinine appears to decrease and cinchonine to increase in amount, although the root bark is generally richer in alkaloids than that of the stem.
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  • The root is diarch in structure, but additional protoxylem-strands may be present at the base of the main root; the pericycle consists of several layers of cells.
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  • The annual rings in a root are often less clearly marked than in the stem, and the xylem-elements are frequently larger and thinner.
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  • A black spot at the root of the pectoral fin is also very characteristic of this species, and but rarely absent.
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  • This was St Francis's root idea, and there is no doubt - though it has been disputed - that it was borrowed from him by St Dominic and the other Mendicant founders.
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  • In an anonymous tract published shortly afterwards (Risposta di un Dottore in Teologia) he laid down principles which struck at the very root of the pope's authority in secular things.
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  • In open places that height is seldom more than about one and a half times the square root of the " fetch " or greatest distance in nautical miles from which the wave has travelled to the point in question; but in narrow reaches or lakes it is relatively higher.
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  • The cultivation of the turnip and other root crops, which require the soil to be wrought to a deep and free tilth, either becomes altdgether impracticable and must be abandoned for the safe but costly bare fallow, or is carried out with great labour and hazard; and the crop, when grown, can neither be removed from the ground, nor consumed upon it by sheep without damage by "poaching."
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  • The iguanas are characterized by the peculiar form of their teeth, these being round at the root and blade-like, with serrated edges towards the tip, resembling in this respect the gigantic extinct reptile Iguanodon.
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  • They are chiefly manifested in the form and number of the horns, which may be increased from the normal two to four or even eight, or may be altogether absent in the female alone or in both sexes; in the shape and length of the ears, which often hang pendent by the side of the head; in the peculiar elevation or arching of the nasal bones in some eastern races; in the length of the tail, and the development of great masses of fat at each side of its root or in the tail itself; and in the colour and quality of the fleece.
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  • If we know p and N, n is called the pth root of N, so that n is the second (or square) root of n 2, the third (or cube) root of n 3, the fourth root of n 4,.
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  • Even where the decimal notation would seem to arise naturally, as in the case of approximate extraction of a square root, the portion which might have been expressed as a decimal was converted into sexagesimal fractions.
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  • The pth root of a number (§43) may, if the number is an integer, be found by expressing it in terms of its prime factors; or, if it is not an integer, by expressing it as a fraction in its lowest terms, and finding the pth roots of the numerator and of the denominator separately.
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  • Thus to find the cube root of 1728, we write it in the form 2.3, and find that its cube root is 2.3=12; or, to find the cube root of 1 728, we write it as 17 r - _ 21_ s_ _ 2'.33.
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  • Similarly the cube root of 2197 is 13.
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  • A number of this kind is called a surd; the surd which is the pth root of N is written ¦JN, but if the index is 2 it is usually omitted, so that the square root of N is written, /N.
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  • If, for instance, we have found 2 then the value of is found from it by multiplying by the 6th power of the 1000th root of 2.
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  • Calculation of Square Root.-The calculation of the square root of a number depends on the formula (iii) of § 60.
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  • If the complete square root is a+b, the remainder after subtracting a 2 is (2a+b)b.
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  • If this is equal to the remainder, we have found the square root.
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  • If it exceeds the square root, we must alter the value of b, so as to get a product which does not exceed the remainder.
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  • If the product is less than the remainder, we get a new remainder, which is N-(a+b) 2; we then assume the full square root to be c, so that the new remainder is equal to (2a+ 2b+c) c, and try to find c in the same way as we tried to find b.
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  • An analogous method of finding cube root, based on the formula for (a+b) 3, used to be given in text-books, but it is of no practical use.
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  • To find a root other than a square root we can use logarithms, as explained in § 113.
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  • Logarithms.-Multiplication, division, involution and evolution, when the results cannot be exact, are usually most simply performed, at any rate to a first approximation, by means of a table of logarithms. Thus, to find the square root of 2, we have log A /2 = log (21)=1 log 2.
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  • More generally, if we have obtained a as an approximate value for the pth root of N, the binomial theorem gives as an approximate formula p,IN =a+6, where N = a P + pap - 19.
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  • The church that they founded struck root, as that of Paulinus and Edwin had failed to do, and was not wrecked even by Oswalds deatn in battle at the hands of Penda the Mercian, the one strong champion of heathenism that England produced.
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  • The mendicants, Dominican and Franciscan, took rapid root in England; the number of friaries erected in the reign of Henry III.
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  • The root of the Hundred Years War, now just about to commence, must be sought in the affairs of Guienne, and not in any of the other causes which complicated and obscured the outbreak of hostilities.
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  • The woollen manufactures which had begun in the eastern counties in the 14th century were now spreading all over the land, taking root especially in Somersetshire, Yorkshire and some districts of the Manufac- Midlands.
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  • The sect spread in a few years to London, Oxford and other centres of intellectual life, but for many years its followers were not numerous; like the old Lollardy, Protestantism took root only in certain places and among certain classesnotably the lesser clergy and the merchants of the great towns.
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